The cost of 21 pencils and 9 pens is Rs. 276, and the cost of 6 pencils and 3 pens is Rs. 84. The cost of 1 pencil and 1 pen is:

Correct option is A

Given:

Cost of 21 pencils and 9 pens = Rs. 276

Cost of 6 pencils and 3 pens = Rs. 84

Solution:

Let the cost of one pencil be Rs x and pen be Rs y.

So, as per the question,

21x + 9y = 276 (1)

6x + 3y = 84 (2)

From (1), we get

​$$x = \frac{276 - 9y}{21}$$​​

From (2), we get

​$$x = \frac{84 - 3y}{6}$$​​

Equating both the equations, we get

​$$\frac{276 - 9y}{21} = \frac{84 - 3y}{6}\\\Rightarrow 6(276 - 9y) = 21(84 - 3y)\\\Rightarrow 1656 - 54y = 1764 - 63y\\\\\Rightarrow -54y + 63y = 1764 - 1656\\\Rightarrow 9y = 108\\\Rightarrow y = \frac{108}{9} = 12\\\text{So, } x = \frac{84 - 3 \times 12}{6} = \frac{84 - 36}{6} = \frac{48}{6} = 8$$​​

Cost of 1 pencil, x = Rs 8

Cost of 1 pen, y = Rs 12.

Total cost = 12 + 8 = Rs 20.